#### Question

# Please Help! Factor The Following...?

Factor:

x^2 - 7x + 12 = 0

I'm STUMPED on how to factor this, if someone could help me and show their steps I will happily give them thumbs up and best answer.

Thank You

#### Answers

Start with what you know and fill in the factors:

Since the x^2 has a coefficient of 1, an x goes in each factor:

(x +- ?)(x +- ?)

Since the constant, 12, is positive, the signs in the factors are the same. Since the x term has a negative coefficient, both signs are minus:

(x - ?)(x - ?)

Now you need two factors of 12 which add to 7. The numbers 3 and 4 will work:

(x - 3)(x - 4)

#1

(x-3)(x-4)

#2

Factors of 12 are 3 and 4.

Middle term is -7, which is -3 + -4, and munus times minus is plus, so

factors are (x-3)(x-4) = 0

x-values are 3 and 4.

#3